Subgroups — C₂×C₁₃×D₁₅₉ #22551990

Order 8268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₅₃	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₅₃	D₃	1	1	yes	characteristic, complemented
6	C₁₃×D₅₃	—	3	2	no	—
7	C₁₃×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₁₅₉	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×D₅₃	—	3	1	no	Hall
12	C₃×C₅₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃×C₁₃	—	53	1	no	maximal, Hall
14	C₂×C₅₃	D₃×C₁₃	1	1	yes	characteristic, complemented
15	D₅₃	—	3	2	no	—
16	C₂×C₃×C₁₃	D₅₃	1	1	yes	characteristic, complemented
17	D₃×C₁₃	—	53	2	no	—
18	C₅₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₃	—	159	1	no	Hall
20	C₃×C₁₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	—	159	2	no	—
22	C₂×C₁₃	D₁₅₉	1	1	yes	characteristic, direct product factor
23	C₁₃	C₂×D₁₅₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	—	53	1	no	Hall
25	C₂×C₃	C₁₃×D₅₃	1	1	yes	characteristic, complemented
26	D₃	—	53	2	no	—
27	C₂²	—	159	1	no	Sylow
28	C₃	C₂×C₁₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	159	2	no	—
30	C₂	C₁₃×D₁₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₁₅₉
commutator, hypocenter	C₃×C₅₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₅₃	C₂
LCS	G ▷ C₃×C₅₃
UCS	C₁ ◁ C₂×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×D₁₅₉	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₅₃	C₂	semidirect
4. C₃×C₁₃×C₅₃	C₂²	semidirect
5. C₂×C₁₃×C₅₃	D₃	semidirect
7. C₁₃×C₅₃	C₂×D₃	semidirect
8. C₂×D₁₅₉	C₁₃	direct (N × H)
9. C₂×C₃×C₅₃	C₂×C₁₃	semidirect
10. D₁₅₉	C₂×C₁₃	direct (N × H)
12. C₃×C₅₃	C₂²×C₁₃	semidirect
14. C₂×C₅₃	D₃×C₁₃	semidirect
16. C₂×C₃×C₁₃	D₅₃	semidirect
18. C₅₃	C₂×D₃×C₁₃	semidirect
20. C₃×C₁₃	C₂×D₅₃	semidirect
22. C₂×C₁₃	D₁₅₉	direct (N × H)
23. C₁₃	C₂×D₁₅₉	direct (N × H)
25. C₂×C₃	C₁₃×D₅₃	semidirect
28. C₃	C₂×C₁₃×D₅₃	semidirect
30. C₂	C₁₃×D₁₅₉	direct (N × H)

Subgroups — C2×C13×D159 #22551990

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×D₁₅₉ #22551990